Subgroups — #30613489

Order 15616.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462656	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#11758217	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461462	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461455	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461440	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461436	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461424	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461420	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461415	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×#92420	C₂	1	1	yes	maximal, characteristic, complemented
11	#21461383	C₂	1	1	yes	maximal, characteristic, complemented
12	#21461158	C₂	1	1	yes	maximal, characteristic, complemented
13	#21461154	C₂	1	1	yes	maximal, characteristic, complemented
14	#21461042	C₂	1	1	yes	maximal, characteristic, complemented
15	AGL(1,ℤ/8)×Dic₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11758217	—	2	1	no	—
17	#16840813	C₂²	1	1	yes	characteristic, complemented
18	#16840813	C₂²	1	1	yes	characteristic, complemented
19	#16840797	C₂²	1	1	yes	characteristic
20	#16840797	C₂²	1	1	yes	characteristic
21	#16840793	—	2	1	no	—
22	#16840793	—	2	1	no	—
23	#16840793	—	2	1	no	—
24	#16840793	—	2	1	no	—
25	D₄×#92420	C₂²	1	1	yes	characteristic
26	D₄×#92420	C₂²	1	1	yes	characteristic
27	D₄×#92420	C₂²	1	1	yes	characteristic, complemented
28	D₄×#92420	C₂²	1	1	yes	characteristic, complemented
29	#16840783	C₂²	1	1	yes	characteristic
30	#16840782	—	2	1	no	—
31	#16840765	C₂²	1	1	yes	characteristic
32	#16840732	—	2	1	no	—
33	C₄×#11758217	C₂²	1	1	yes	characteristic
34	C₄×#11758217	C₂²	1	1	yes	characteristic
35	C₂×#14519832	—	2	1	no	—
36	#16840626	C₂²	1	1	yes	characteristic, complemented
37	#16840625	C₂²	1	1	yes	characteristic, complemented
38	#16840624	C₂²	1	1	yes	characteristic, complemented
39	#16840623	C₂²	1	1	yes	characteristic, complemented
40	Q₈⋊#92420	C₂²	1	1	yes	characteristic, complemented
41	Q₈⋊#92420	C₂²	1	1	yes	characteristic, complemented
42	D₄⋊#92420	C₂²	1	1	yes	characteristic
43	D₄⋊#92420	C₂²	1	1	yes	characteristic
44	D₄⋊#92420	C₂²	1	1	yes	characteristic
45	D₄⋊#92420	C₂²	1	1	yes	characteristic
46	D₄⋊#92420	C₂²	1	1	yes	characteristic, complemented
47	D₄⋊#92420	C₂²	1	1	yes	characteristic, complemented
48	#92420⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	#92420⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	#16840603	C₂²	1	1	yes	characteristic, complemented
51	C₈×#92420	C₂²	1	1	yes	characteristic, complemented
52	#41×Dic₆₁	C₂²	1	1	yes	characteristic
53	C₂×D₄×Dic₆₁	C₂²	1	1	yes	characteristic
54	#16839874	C₄	1	1	yes	characteristic
55	#16839874	C₄	1	1	yes	characteristic
56	#16839863	C₄	1	1	yes	characteristic
57	#16839863	C₄	1	1	yes	characteristic
58	SD₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
59	SD₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
60	D₈×Dic₆₁	C₂²	1	1	yes	characteristic
61	D₈×Dic₆₁	C₂²	1	1	yes	characteristic
62	#16839804	C₄	1	1	yes	characteristic
63	#16839767	C₄	1	1	yes	characteristic
64	#16839763	C₄	1	1	yes	characteristic
65	M₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
66	C₂×AGL(1,ℤ/8)×C₆₁	C₄	1	1	yes	characteristic
67	C₂×#11758217	—	2	1	no	—
68	C₂×#11758217	—	2	1	no	—
69	C₂×#11758217	—	2	1	no	—
70	C₂×#11758217	—	2	1	no	—
71	C₂×#11758217	—	4	4	no	—
72	C₂×#11758217	D₄	1	1	yes	characteristic
73	C₂×#11758217	D₄	1	1	yes	characteristic
74	C₂²×#92420	—	2	1	no	—
75	C₂²×#92420	—	2	1	no	—
76	C₂²×#92420	—	2	1	no	—
77	C₂²×#92420	—	2	1	no	—
78	#14519844	—	2	1	no	—
79	#14519844	—	2	1	no	—
80	#14519844	—	2	1	no	—
81	C₄⋊#92420	C₂³	1	1	yes	characteristic
82	C₄⋊#92420	C₂³	1	1	yes	characteristic
83	C₄⋊#92420	C₂³	1	1	yes	characteristic
84	C₄⋊#92420	C₂³	1	1	yes	characteristic
85	C₂²⋊#92420	—	2	1	no	—
86	C₂²⋊#92420	—	2	1	no	—
87	C₂²⋊#92420	—	2	1	no	—
88	C₂²⋊#92420	—	2	1	no	—
89	C₂²⋊#92420	—	2	1	no	—
90	C₂²⋊#92420	—	2	1	no	—
91	C₂²⋊#92420	—	2	1	no	—
92	#14519832	—	2	1	no	—
93	#14519832	—	2	1	no	—
94	#14519832	—	2	1	no	—
95	#14519832	—	2	1	no	—
96	#14519832	D₄	1	1	yes	characteristic
97	#14519832	D₄	1	1	yes	characteristic
98	C₄×#92420	C₂³	1	1	yes	characteristic
99	C₄×#92420	C₂³	1	1	yes	characteristic
100	C₄×#92420	C₂³	1	1	yes	characteristic
101	C₄×#92420	C₂³	1	1	yes	characteristic
102	C₂³×Dic₆₁	—	2	1	no	—
103	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
104	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
105	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
106	D₄×Dic₆₁	—	2	1	no	—
107	D₄×Dic₆₁	—	2	1	no	—
108	D₄×Dic₆₁	—	2	1	no	—
109	D₄×Dic₆₁	—	2	1	no	—
110	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
111	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
112	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
113	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
114	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
115	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
116	#14519736	—	2	1	no	—
117	#14519736	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊Dic₆₁	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊Dic₆₁	—	2	1	no	—
120	C₂×C₄×Dic₆₁	—	2	1	no	—
121	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
122	#14519711	C₂×C₄	1	1	yes	characteristic
123	#14519711	C₂×C₄	1	1	yes	characteristic
124	#14519709	C₂×C₄	1	1	yes	characteristic
125	#14519709	C₂×C₄	1	1	yes	characteristic
126	#14519701	C₂×C₄	1	1	yes	characteristic
127	#14519701	C₂×C₄	1	1	yes	characteristic
128	#14519698	C₂×C₄	1	1	yes	characteristic
129	#14519698	C₂×C₄	1	1	yes	characteristic
130	#14519698	C₂×C₄	1	1	yes	characteristic
131	#14519698	C₂×C₄	1	1	yes	characteristic
132	#14519698	C₂×C₄	1	1	yes	characteristic
133	#14519698	C₂×C₄	1	1	yes	characteristic
134	#14519687	C₂×C₄	1	1	yes	characteristic
135	#14519687	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
137	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
139	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
140	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
141	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
142	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
143	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic
144	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic
145	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
146	C₂⁴×C₆₁	—	2	1	no	—
147	#41×C₆₁	—	2	2	no	—
148	#41×C₆₁	—	4	1	no	—
149	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₄×C₆₁	—	2	2	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	—	4	1	no	—
154	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×Dic₆₁	—	2	1	no	—
160	C₂²×Dic₆₁	—	2	1	no	—
161	C₂²×Dic₆₁	—	2	1	no	—
162	C₂²×Dic₆₁	—	2	1	no	—
163	C₂²×Dic₆₁	—	2	1	no	—
164	C₂²×Dic₆₁	—	2	1	no	—
165	C₂²×Dic₆₁	—	2	1	no	—
166	C₂²×Dic₆₁	—	4	2	no	—
167	C₂²×Dic₆₁	—	4	2	no	—
168	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×Dic₆₁	#41	1	1	yes	characteristic
170	#11758217	—	2	2	no	—
171	#11758217	—	4	1	no	—
172	#11758217	—	4	2	no	—
173	#11758217	—	4	2	no	—
174	#11758217	—	4	2	no	—
175	#11758217	—	4	2	no	—
176	C₂×#92420	—	2	1	no	—
177	C₂×#92420	—	2	1	no	—
178	C₂×#92420	—	2	1	no	—
179	C₂×#92420	—	2	1	no	—
180	C₂×#92420	—	2	1	no	—
181	C₂×#92420	—	2	1	no	—
182	C₂×#92420	—	4	2	no	—
183	C₂×#92420	—	4	2	no	—
184	C₂×#92420	—	4	2	no	—
185	C₂×#92420	—	4	2	no	—
186	C₂×#92420	C₂×D₄	1	1	yes	characteristic
187	C₂×#92420	C₂×D₄	1	1	yes	characteristic
188	C₂×#92420	C₂×D₄	1	1	yes	characteristic
189	C₂×#92420	C₂×D₄	1	1	yes	characteristic
190	SD₁₆×C₆₁	—	2	2	no	—
191	SD₁₆×C₆₁	—	2	2	no	—
192	D₈×C₆₁	—	2	2	no	—
193	D₈×C₆₁	M₁₆	1	4	yes	complemented
194	M₁₆×C₆₁	—	2	2	no	—
195	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊Dic₆₁	—	2	1	no	—
198	C₂²⋊Dic₆₁	—	2	1	no	—
199	C₂²⋊Dic₆₁	—	2	1	no	—
200	C₂²⋊Dic₆₁	—	2	1	no	—
201	C₂²⋊Dic₆₁	—	2	1	no	—
202	C₂²⋊Dic₆₁	—	2	1	no	—
203	C₂²⋊Dic₆₁	—	2	1	no	—
204	C₄⋊Dic₆₁	—	2	1	no	—
205	C₄⋊Dic₆₁	—	2	1	no	—
206	C₄⋊Dic₆₁	—	2	1	no	—
207	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₆₁	—	2	1	no	—
212	C₄×Dic₆₁	—	2	1	no	—
213	C₄×Dic₆₁	—	2	1	no	—
214	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
216	C₄×Dic₆₁	#41	1	1	yes	characteristic
217	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
218	#11758194	—	4	1	no	—
219	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
220	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
221	C₂³×C₆₁	—	2	1	no	—
222	C₂³×C₆₁	—	2	1	no	—
223	C₂³×C₆₁	—	2	1	no	—
224	C₂³×C₆₁	—	4	2	no	—
225	C₂³×C₆₁	—	4	2	no	—
226	C₂³×C₆₁	—	8	1	no	—
227	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
228	Q₈×C₆₁	—	2	1	no	—
229	Q₈×C₆₁	—	2	1	no	—
230	D₄×C₆₁	—	2	1	no	—
231	D₄×C₆₁	—	2	1	no	—
232	D₄×C₆₁	—	2	1	no	—
233	D₄×C₆₁	—	2	1	no	—
234	D₄×C₆₁	—	4	2	no	—
235	D₄×C₆₁	—	4	2	no	—
236	D₄×C₆₁	C₂×M₁₆	1	2	yes	—
237	D₄×C₆₁	C₂×M₁₆	1	2	yes	complemented
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	4	2	no	—
242	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
244	C₂×Dic₆₁	—	2	1	no	—
245	C₂×Dic₆₁	—	2	1	no	—
246	C₂×Dic₆₁	—	2	1	no	—
247	C₂×Dic₆₁	—	2	1	no	—
248	C₂×Dic₆₁	—	2	1	no	—
249	C₂×Dic₆₁	—	2	1	no	—
250	C₂×Dic₆₁	—	4	1	no	—
251	C₂×Dic₆₁	—	4	2	no	—
252	C₂×Dic₆₁	—	4	2	no	—
253	C₂×Dic₆₁	—	4	2	no	—
254	C₂×Dic₆₁	—	4	1	no	—
255	C₂×Dic₆₁	—	4	1	no	—
256	C₂×Dic₆₁	—	4	1	no	—
257	C₂×Dic₆₁	—	4	1	no	—
258	C₂×Dic₆₁	—	4	1	no	—
259	C₂×Dic₆₁	—	4	1	no	—
260	C₂×Dic₆₁	—	8	1	no	—
261	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
262	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
263	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
264	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
265	#92420	—	2	2	no	—
266	#92420	—	2	1	no	—
267	#92420	—	2	1	no	—
268	#92420	—	2	1	no	—
269	#92420	—	4	1	no	—
270	#92420	—	4	1	no	—
271	#92420	—	4	1	no	—
272	#92420	—	4	1	no	—
273	#92420	—	4	1	no	—
274	#92420	AGL(1,ℤ/8)	1	2	yes	complemented
275	C₈×C₆₁	—	2	1	no	—
276	C₈×C₆₁	C₂×M₁₆	1	2	yes	complemented
277	#92418	—	2	1	no	—
278	#92418	—	2	1	no	—
279	#18046	—	61	1	no	maximal, Sylow
280	C₂²×C₆₁	—	2	1	no	—
281	C₂²×C₆₁	—	2	2	no	—
282	C₂²×C₆₁	—	2	2	no	—
283	C₂²×C₆₁	—	2	1	no	—
284	C₂²×C₆₁	—	2	1	no	—
285	C₂²×C₆₁	—	4	1	no	—
286	C₂²×C₆₁	—	4	1	no	—
287	C₂²×C₆₁	—	4	1	no	—
288	C₂²×C₆₁	—	4	1	no	—
289	C₂²×C₆₁	—	4	1	no	—
290	C₂²×C₆₁	—	4	1	no	—
291	C₂²×C₆₁	—	4	1	no	—
292	C₂²×C₆₁	—	8	4	no	—
293	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₆₁	—	2	1	no	—
295	C₄×C₆₁	—	4	1	no	—
296	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
297	C₄×C₆₁	#568	1	1	yes	characteristic
298	Dic₆₁	—	2	1	no	—
299	Dic₆₁	—	2	1	no	—
300	Dic₆₁	—	2	1	no	—
301	Dic₆₁	—	4	1	no	—
302	Dic₆₁	—	4	1	no	—
303	Dic₆₁	—	4	1	no	—
304	Dic₆₁	—	4	1	no	—
305	Dic₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	Dic₆₁	#575	1	1	yes	characteristic
307	#2970	—	61	1	no	—
308	C₄×AGL(1,ℤ/8)	—	61	1	no	—
309	D₄×M₁₆	—	61	1	no	—
310	#1592	—	61	1	no	—
311	#1590	—	61	1	no	—
312	#1586	—	61	1	no	—
313	#1585	—	61	1	no	—
314	#1582	—	61	1	no	—
315	#1581	—	61	1	no	—
316	#1580	—	61	1	no	—
317	C₈×D₈	—	61	1	no	—
318	#1569	—	61	1	no	—
319	#1490	—	61	1	no	—
320	#1489	—	61	1	no	—
321	#1455	—	61	1	no	—
322	C₂×C₆₁	—	4	1	no	—
323	C₂×C₆₁	—	4	2	no	—
324	C₂×C₆₁	—	4	2	no	—
325	C₂×C₆₁	—	8	1	no	—
326	C₂×C₆₁	D₄×M₁₆	1	1	yes	characteristic
327	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₂×C₆₁	#2956	1	1	yes	characteristic
329	C₂×AGL(1,ℤ/8)	#6923	1	1	yes	characteristic
330	C₂²×M₁₆	—	122	1	no	—
331	C₄×#41	—	61	1	no	—
332	C₂×C₄×D₄	—	61	1	no	—
333	#446	—	61	1	no	—
334	#446	—	61	1	no	—
335	#442	—	61	1	no	—
336	#442	—	61	1	no	—
337	#440	—	61	1	no	—
338	#440	—	61	1	no	—
339	C₄×SD₁₆	—	61	1	no	—
340	C₄×SD₁₆	—	61	1	no	—
341	C₄×D₈	—	61	1	no	—
342	C₄×D₈	—	61	1	no	—
343	#436	—	61	1	no	—
344	#436	—	61	1	no	—
345	#435	—	122	1	no	—
346	#435	—	122	1	no	—
347	#435	—	122	1	no	—
348	#435	—	122	1	no	—
349	C₈×D₄	—	61	1	no	—
350	C₈×D₄	—	61	1	no	—
351	C₈×D₄	—	61	1	no	—
352	C₈×D₄	—	61	1	no	—
353	#432	—	61	1	no	—
354	#432	—	122	1	no	—
355	#428	—	61	1	no	—
356	#423	—	61	1	no	—
357	#418	—	61	1	no	—
358	#417	—	61	1	no	—
359	#407	—	122	1	no	—
360	C₄×M₁₆	—	61	1	no	—
361	C₄×M₁₆	—	61	1	no	—
362	C₄×M₁₆	—	61	1	no	—
363	C₂×#97	—	122	1	no	—
364	#335	—	61	1	no	—
365	#335	—	61	1	no	—
366	#334	—	61	1	no	—
367	#334	—	61	1	no	—
368	Q₈⋊C₈	—	61	1	no	—
369	Q₈⋊C₈	—	61	1	no	—
370	D₄⋊C₈	—	61	1	no	—
371	D₄⋊C₈	—	61	1	no	—
372	D₄⋊C₈	—	61	1	no	—
373	D₄⋊C₈	—	61	1	no	—
374	D₄⋊C₈	—	61	1	no	—
375	D₄⋊C₈	—	61	1	no	—
376	#322	—	61	1	no	—
377	#322	—	61	1	no	—
378	#322	—	61	1	no	—
379	C₈²	—	61	1	no	—
380	C₆₁	#18046	1	1	yes	characteristic, complemented, Sylow
381	C₂×#41	C₂×#6923	1	1	yes	characteristic
382	C₂²×D₄	C₂×#6923	1	1	yes	characteristic
383	C₂³×C₄	—	122	1	no	—
384	AGL(1,ℤ/8)	—	2	4	no	—
385	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
386	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
387	C₂×D₈	C₂×#6923	1	1	yes	characteristic
388	C₂×D₈	C₂×#6923	1	1	yes	characteristic
389	C₂×M₁₆	—	61	1	no	—
390	C₂×M₁₆	—	61	1	no	—
391	C₂×M₁₆	—	61	1	no	—
392	C₂×M₁₆	—	122	1	no	—
393	C₂×M₁₆	—	122	1	no	—
394	C₂×M₁₆	—	122	1	no	—
395	C₂×M₁₆	—	122	1	no	—
396	C₂×M₁₆	—	244	4	no	—
397	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
398	C₂²×C₈	—	122	1	no	—
399	C₂²×C₈	—	122	1	no	—
400	C₂²×C₈	—	122	1	no	—
401	C₂²×C₈	—	122	1	no	—
402	C₄×Q₈	—	61	1	no	—
403	C₄×Q₈	—	61	1	no	—
404	C₄×D₄	—	61	1	no	—
405	C₄×D₄	—	61	1	no	—
406	C₄×D₄	—	61	1	no	—
407	C₄×D₄	—	61	1	no	—
408	C₄×D₄	—	61	1	no	—
409	C₄×D₄	—	61	1	no	—
410	C₄×D₄	—	122	1	no	—
411	C₄×D₄	—	122	1	no	—
412	C₄×D₄	—	122	1	no	—
413	C₄×D₄	—	122	1	no	—
414	#117	—	61	1	no	—
415	#117	—	122	1	no	—
416	C₂×C₄⋊C₄	—	61	1	no	—
417	C₂×C₂²⋊C₄	—	122	1	no	—
418	C₂×C₄²	—	61	1	no	—
419	C₂×C₄²	—	122	1	no	—
420	#107	—	61	1	no	—
421	#107	—	61	1	no	—
422	#106	—	61	1	no	—
423	#106	—	61	1	no	—
424	C₄⋊C₈	—	61	1	no	—
425	C₄⋊C₈	—	61	1	no	—
426	C₄⋊C₈	—	61	1	no	—
427	C₄⋊C₈	—	61	1	no	—
428	C₄⋊C₈	—	122	1	no	—
429	C₄⋊C₈	—	122	1	no	—
430	C₄⋊C₈	—	122	1	no	—
431	#103	—	61	1	no	—
432	#103	—	61	1	no	—
433	#102	—	61	1	no	—
434	#102	—	61	1	no	—
435	#102	—	61	1	no	—
436	#102	—	61	1	no	—
437	#102	—	61	1	no	—
438	#102	—	61	1	no	—
439	C₂²⋊C₈	—	122	1	no	—
440	C₂²⋊C₈	—	122	1	no	—
441	C₂²⋊C₈	—	122	1	no	—
442	C₂²⋊C₈	—	122	1	no	—
443	C₂²⋊C₈	—	122	1	no	—
444	C₂²⋊C₈	—	122	1	no	—
445	C₂²⋊C₈	—	122	1	no	—
446	#97	—	61	1	no	—
447	#97	—	61	1	no	—
448	#97	—	61	1	no	—
449	#97	—	61	1	no	—
450	#97	—	122	1	no	—
451	#97	—	122	1	no	—
452	#97	—	122	1	no	—
453	#97	—	122	1	no	—
454	C₄×C₈	—	61	1	no	—
455	C₄×C₈	—	61	1	no	—
456	C₄×C₈	—	61	1	no	—
457	C₄×C₈	—	61	1	no	—
458	C₄×C₈	—	61	1	no	—
459	C₄×C₈	—	61	1	no	—
460	C₂⁴	—	2	1	no	—
461	#41	—	2	2	no	—
462	#41	—	4	1	no	—
463	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
469	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
470	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	61	1	no	—
473	C₂²×C₄	—	61	1	no	—
474	C₂²×C₄	—	122	1	no	—
475	C₂²×C₄	—	122	1	no	—
476	C₂²×C₄	—	122	1	no	—
477	C₂²×C₄	—	122	1	no	—
478	C₂²×C₄	—	122	1	no	—
479	C₂²×C₄	—	122	1	no	—
480	C₂²×C₄	—	122	1	no	—
481	C₂²×C₄	—	244	2	no	—
482	C₂²×C₄	—	244	2	no	—
483	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
484	SD₁₆	—	2	2	no	—
485	SD₁₆	—	2	2	no	—
486	D₈	—	2	2	no	—
487	D₈	#11758217	1	4	yes	complemented
488	M₁₆	—	2	2	no	—
489	M₁₆	—	122	2	no	—
490	M₁₆	—	244	2	no	—
491	M₁₆	—	244	1	no	—
492	M₁₆	—	244	1	no	—
493	M₁₆	—	244	2	no	—
494	M₁₆	—	244	2	no	—
495	M₁₆	—	244	2	no	—
496	C₂×C₈	—	61	1	no	—
497	C₂×C₈	—	61	1	no	—
498	C₂×C₈	—	61	1	no	—
499	C₂×C₈	—	61	1	no	—
500	C₂×C₈	—	61	1	no	—
501	C₂×C₈	—	61	1	no	—
502	C₂×C₈	—	122	1	no	—
503	C₂×C₈	—	122	1	no	—
504	C₂×C₈	—	122	1	no	—
505	C₂×C₈	—	122	1	no	—
506	C₂×C₈	—	122	1	no	—
507	C₂×C₈	—	122	1	no	—
508	C₂×C₈	—	244	2	no	—
509	C₂×C₈	—	244	2	no	—
510	C₂×C₈	—	244	2	no	—
511	C₂×C₈	—	244	2	no	—
512	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
513	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
514	C₄⋊C₄	—	61	1	no	—
515	C₄⋊C₄	—	61	1	no	—
516	C₄⋊C₄	—	61	1	no	—
517	C₄⋊C₄	—	61	1	no	—
518	C₄⋊C₄	—	122	1	no	—
519	C₄⋊C₄	—	122	1	no	—
520	C₄⋊C₄	—	122	1	no	—
521	C₂²⋊C₄	—	122	1	no	—
522	C₂²⋊C₄	—	122	1	no	—
523	C₂²⋊C₄	—	122	1	no	—
524	C₂²⋊C₄	—	122	1	no	—
525	C₂²⋊C₄	—	122	1	no	—
526	C₂²⋊C₄	—	122	1	no	—
527	C₂²⋊C₄	—	122	1	no	—
528	C₄²	—	61	1	no	—
529	C₄²	—	61	1	no	—
530	C₄²	—	61	1	no	—
531	C₄²	—	61	1	no	—
532	C₄²	—	122	1	no	—
533	C₄²	—	122	1	no	—
534	C₄²	—	122	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	8	1	no	—
541	C₂³	D₄×#6923	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	C₂×#11758217	1	2	yes	—
551	D₄	C₂×#11758217	1	2	yes	complemented
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	61	1	no	—
557	C₂×C₄	—	61	1	no	—
558	C₂×C₄	—	61	1	no	—
559	C₂×C₄	—	61	1	no	—
560	C₂×C₄	—	122	1	no	—
561	C₂×C₄	—	122	1	no	—
562	C₂×C₄	—	122	1	no	—
563	C₂×C₄	—	122	1	no	—
564	C₂×C₄	—	122	1	no	—
565	C₂×C₄	—	122	1	no	—
566	C₂×C₄	—	488	1	no	—
567	C₂×C₄	—	244	1	no	—
568	C₂×C₄	—	244	1	no	—
569	C₂×C₄	—	244	1	no	—
570	C₂×C₄	—	244	1	no	—
571	C₂×C₄	—	244	1	no	—
572	C₂×C₄	—	244	1	no	—
573	C₂×C₄	—	244	1	no	—
574	C₂×C₄	—	244	2	no	—
575	C₂×C₄	—	244	2	no	—
576	C₂×C₄	—	244	2	no	—
577	C₂×C₄	D₄×#6923	1	1	yes	characteristic
578	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
579	C₈	—	2	1	no	—
580	C₈	—	61	2	no	—
581	C₈	—	122	1	no	—
582	C₈	—	122	1	no	—
583	C₈	—	122	1	no	—
584	C₈	—	122	2	no	—
585	C₈	—	122	1	no	—
586	C₈	—	122	1	no	—
587	C₈	—	244	1	no	—
588	C₈	—	244	1	no	—
589	C₈	—	244	1	no	—
590	C₈	—	244	1	no	—
591	C₈	—	244	1	no	—
592	C₈	C₂×#11758217	1	2	yes	complemented
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	8	4	no	—
606	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	61	1	no	—
610	C₄	—	61	1	no	—
611	C₄	—	122	1	no	—
612	C₄	—	122	1	no	—
613	C₄	—	122	1	no	—
614	C₄	—	244	1	no	—
615	C₄	—	244	1	no	—
616	C₄	—	244	1	no	—
617	C₄	—	244	1	no	—
618	C₄	C₂²×#11758217	1	1	yes	characteristic
619	C₄	#16840840	1	1	yes	characteristic
620	C₂	—	4	1	no	—
621	C₂	—	4	2	no	—
622	C₂	—	4	2	no	—
623	C₂	—	8	1	no	—
624	C₂	D₄×#11758217	1	1	yes	characteristic
625	C₂	AGL(1,ℤ/8)×#6923	1	1	yes	characteristic
626	C₂	#21462593	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting, prime radical	C₂×AGL(1,ℤ/8)×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	C₂×AGL(1,ℤ/8)	#6923
hypocenter	C₆₁	#18046
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #21462656	C₂	semidirect
2. D₄×#11758217	C₂	semidirect
3. #21461462	C₂	semidirect
4. #21461455	C₂	semidirect
5. #21461440	C₂	semidirect
6. #21461436	C₂	semidirect
7. #21461424	C₂	semidirect
8. #21461420	C₂	semidirect
9. #21461415	C₂	semidirect
10. D₈×#92420	C₂	semidirect
11. #21461383	C₂	semidirect
12. #21461158	C₂	semidirect
13. #21461154	C₂	semidirect
14. #21461042	C₂	semidirect
17. #16840813	C₂²	semidirect
18. #16840813	C₂²	semidirect
27. D₄×#92420	C₂²	semidirect
28. D₄×#92420	C₂²	semidirect
36. #16840626	C₂²	semidirect
37. #16840625	C₂²	semidirect
38. #16840624	C₂²	semidirect
39. #16840623	C₂²	semidirect
40. Q₈⋊#92420	C₂²	semidirect
41. Q₈⋊#92420	C₂²	semidirect
46. D₄⋊#92420	C₂²	semidirect
47. D₄⋊#92420	C₂²	semidirect
48. #92420⋊C₈	C₂²	semidirect
49. #92420⋊C₈	C₂²	semidirect
50. #16840603	C₂²	semidirect
51. C₈×#92420	C₂²	semidirect
193. D₈×C₆₁	M₁₆	semidirect
237. D₄×C₆₁	C₂×M₁₆	semidirect
274. #92420	AGL(1,ℤ/8)	semidirect
276. C₈×C₆₁	C₂×M₁₆	semidirect
380. C₆₁	#18046	semidirect
487. D₈	#11758217	semidirect
551. D₄	C₂×#11758217	semidirect
592. C₈	C₂×#11758217	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21462656	2
D₄×#11758217	2
#21461462	2
#21461455	2
#21461440	2
#21461436	2
#21461424	2
#21461420	2
#21461415	2
D₈×#92420	2
#21461383	2
#21461158	2
#21461154	2
#21461042	2
AGL(1,ℤ/8)×Dic₆₁	2
#18046	61